“FUN” PROBLEM #4

 

   1.   Find a number which is 10 more than its additive inverse. 

   Number = x                                 x= -x + 10                                            the number is 5

   Additive Inverse = -x                     2x = 10

                                                      x = 5

 

   2.   Find a number which is 14 less than its additive inverse.

   Number = x                                 x= -x - 14                                              the number is -7

   Additive Inverse = -x                     2x = -14           

                                                      x = -7

 

   3.   Seven times a certain number is nine less than twice number.  Find the number.

   Number = x                                 7x =   2x - 9                                          the number is -9/5

                                                      5x = -9

                                                      x = -9/5

 

   4.   Seven times a certain number is fourteen more than five times the number.

   Number = x                                 7x = 5x +14                                          the number is 7

                                          2x =14

                                          x = 7

  

   5.   Frank challenged: “Six years ago I was half as old as I am old.  How old am I?”

   Frank present = x             x-6 = 1/2 x                                            12

   Six years ago = x-6                      -6 = -1/2 x

                                          12 = x

 

   6.   Ada declared, “Twenty years from now I will be three times as old as I am now.  How old am I?”

   Present = x                                  x +20 = 3x                                           10                    

   Future = x + 20                           20 = 2x

                                          10 = x

 

   7.   Roger had 6 steel balls of the same size and shape.  He found that when he put 5 of the balls in one pan of a beam balance and put the sixth ball and a 100-gram weight in the other pan, the pans were in balance.  How much did each ball weigh?

   Weight of 1 ball = x                      5x = x+100                                           25

                                          4x = 100

                                          x = 25

 

   8.   Wilma has six coins of the same kind.  A dollar and two of the coins have the same total value as all six coins put together, what kind of coin does Wilma have?

   Value of 1 coin = x                       100 + 2x = 6x                           25 cents

                                          100 = 4x

                                          25 = x

  

   9.   A mother aged 29 has a 5-year old daughter.   In how many years will the mother be four times as old as her daughter?

   How many years future = x                       29 + x = 4(5+x)                                    3

   Mother future= 29+x                    29 + x = 20+4x

   Daughter = 5+x                           9 = 3x

                                                      3 = x

   10.   Fifteen old Al has an uncle who is 43 years old.  How many years ago was the uncle fives times as old as Al was?

   Years past = x                              43-x = 5(15-x)                8

   Al = 15-x                                      43-x = 75-5x

   Uncle = 43-x                                4x = 32

                                                      x = 8